According to the AFP News Agency, party sources from within the German leading coalition have stated that German Interior Minister Horst Seehofer is seeking to resign from his post as Germany's Interior Minister, as well as his seat as the head of Germany's Christian Social Union (CSU), the other half of Germany's CDU/CSU coalition.
"After a tough struggle and some hard days, we've found a really good compromise", said Merkel, who heads the Christian Democratic Union (CDU).
Still Ms. Merkel needs the CSU deputies in parliament to maintain her majority in the three-way coalition with the Social Democrats (SPD).
Germany's constitution prevents federal ministers from outright quitting their positions, and must request to be dismissed by the German President.
The divisions within the German government over the issue are also being played out in other European Union countries, and three countries later said they were not part of the German deal: the Czech Republic, Hungary and Poland.
The border deal, hailed by the German chancellor as a "good compromise", foresees setting up so-called transit centres on the southern border, where asylum seekers who have already been registered in other European Union countries will be held until they can be sent back to those countries.
The proposal could also shift the political crisis south to Austria, where the government said it could take its own measures to protect its borders.
The move appeared to end a political standoff with her interior minister Horst Seehofer which posed the most serious threat yet to her 13-year premiership.
All new migrants would have to be screened at the centers and determined if they are eligible to seek asylum in Germany.
The flashpoint issue was Seehofer's demand to order German border police to immediately turn back all asylum seekers already registered elsewhere in the European Union, and his threat to do so against Merkel's wishes.
The public approval has been largely in favor of Merkel's policies since 2015 but the support started to wane as the country began experiencing problems absorbing the new residents, the Times reported.
As he entered a CDU crisis meeting Monday, party deputy leader Armin Laschet insisted that the sister parties "want to hold onto" their alliance.
He could defy her orders by ordering border police to carry out his plan, which would force her to fire him and nearly certainly break up the CDU-CSU alliance, or he could accept a humiliating climbdown or resign.
That decision convulsed European politics, fueling the rise of anti-immigration parties including the far-right Alternative for Germany (AfD) party, which now threatens to unseat the CSU in October's regional elections.
German politicians who criticized the agreement say Merkel and her conservatives had abandoned the country's moral mission.
But soon after, Seehofer said he would hold last-ditch talks with Merkel's CDU "in hopes of reaching an understanding".
"We will do the same thing and we'll come out ahead because there are more people arriving here".
"As such the spirit of partnership in the European Union is preserved and at the same time an important step to order and control secondary migration and that's why I think that we have found a good compromise after tough negotiations and hard days".